Stereoscopic image display apparatus

ABSTRACT

It is made possible to prevent luminance falling and moire occurrence and change over between a two-dimensional image and a three-dimensional image partially. When displaying one of a three-dimensional image and a two-dimensional image on a background and displaying the other image in a window, a flag bit indicating whether the first and second electrodes overlap the window is set. Waveforms differing according to the flag bit are applied to the first and second electrodes as pulses applied to the opposed first and second electrodes of a variable polarization cell. As a result, three-dimensional image display is partially conducted in the window and two-dimensional image display is conducted in areas other than the window. Or two-dimensional image display is partially conducted in the window and three-dimensional image display is conducted in areas other than the window.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority fromprior Japanese Patent Application No. 2008-243915 filed on Sep. 24, 2008in Japan, the entire contents of which are incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a stereoscopic image display apparatuscapable of displaying one of a two-dimensional image and athree-dimensional image partially when the other of the two-dimensionalimage and the three-dimensional image is being displayed.

2. Related Art

A method of recording a stereoscopic image by using some method andreproducing it as a stereoscopic image is known. This method is calledintegral photography (hereafter referred to as IP method) for displayinga number of parallax images or light ray reproduction method. It issupposed that an object is viewed with left and right eyes. When a pointA located at a short distance is viewed, an angle formed by the point Aand the left and right eyes is denoted by α. When a point B located at along distance is viewed, an angle formed by the point B and the left andright eyes is denoted by β. The angles α and β vary depending upon theposition relation between the object and the viewer. The difference(α−β) is called binocular parallax. Human being is sensitive to thebinocular parallax and is able to conduct stereoscopic viewing.

In recent years, development of stereoscopic image display apparatuseswithout glasses has been promoted. Many of them use the ordinarytwo-dimensional plane display device. Many of them are made possible byplacing some optical plate on the front or back of the plane displaydevice, utilizing the binocular parallax described above, andcontrolling angles of light rays from the plane display device so as tocause light rays to appear to be illuminated from objects locatedseveral cm before and behind the plane display device when viewed by aviewer. This is because it has become possible to obtain an image whichis high in definition to some degree even if light rays of the planedisplay device are distributed to several kinds of angles (calledparallaxes), owing to implementation of the plane display device havinga higher definition.

A three-dimensional (hereafter referred to as 3D as well) display methodimplemented by thus applying the IP method to a stereoscopic imagedisplay device is called integral imaging (II) scheme. In the II scheme,the number of light rays illuminated from one lens corresponds to thenumber of element image groups. The number of the element image groupsis typically called number of parallaxes. In each lens, parallax raysare illuminated in parallel. In the II scheme, the viewer viewsdifferent images: an image of 1 parallax, an image of 2 parallaxes, andan image of 3 parallaxes, according to the position of the viewer or theangle at which the viewer views.

Therefore, the viewer perceives a solid body by parallax between theright eye and the left eye. If a lenticular lens is used as the opticalplate, there is a merit that the display is bright because theutilization efficiency of light is high as compared with a slit. As fora gap between the lens array and pixels, it is desirable to provide adistance which is nearly equal to the focal length. By doing so, onepixel can be illuminated in one direction and parallax images whichdiffer according to the viewing angle can be viewed.

The best-known substance having a double refraction property is calcite.As an optical application of the double refraction, there is a drawnfilm used for the retardation film. Specifically, ARTON (JSRCorporation) and polycarbonate (Nitto Denko Corporation) are well known.

Furthermore, liquid crystal also has the double refraction property. Inthe liquid crystal, each molecule takes a long and slender shape.Anisotropy of the refractive index occurs in a lengthwise direction ofthe molecule called director. For example, many of molecules in nematicliquid crystal are long and slender molecules. Their major axisdirections are aligned and oriented. However, position relations of themolecules are random. Even if the orientation directions of moleculesare in alignment, the absolute temperature of ambience in use is notzero degree, and consequently they are not perfectly parallel and thereis fluctuation (represented by an order parameter S) to some degree.Viewing a local region, however, it can be said that molecules arealigned in nearly one direction. When a region which is small enoughmacroscopically but large enough as compared with the size of the liquidcrystal molecules is supposed, the average orientation direction of themolecules in that region is represented by using a unit vector n, and itis referred to as director or orientation vector. An orientation inwhich the director becomes nearly parallel to the substrate is referredto as homogeneous orientation. One of the greatest features of liquidcrystal is optical anisotropy. Especially, since the degree of freedomin the molecule arrangement is high as compared with other anisotropicmedia such as crystal, the difference in refractive index between themajor axis and the minor axis which is a criterion of double refractionis great.

In simple matrix drive which is one of drive schemes for driving theliquid crystal, a configuration obtained by interposing a liquid crystallayer between row electrodes Xn arranged in one column and columnelectrodes Ym is used. The liquid crystal is activated by selectivelyapplying a voltage to a part (pixels) where these electrodes intersect.In this drive method, electrodes are formed of transparent electrodesand a transistor which individually controls ON-OFF is not provided ineach pixel. Therefore, there are no black matrixes for hiding wires.This results in a merit that the luminance can be made bright.

In active matrix drive which is another drive scheme for driving theliquid crystal, the electro-optic effect itself of the liquid crystal isprovided with a memory property. For example, if a voltage is appliedstationarily over a frame period once changeover from the ON state tothe OFF state is performed, then high definition display becomespossible in principle even when the display capacity is increasedremarkably. As an element having such a memory property, there is anactive element such as a transistor or a diode. In the configurationaccording to the active matrix scheme, the active element is added toeach pixel. A merit of this active matrix scheme is that polarizationchangeover which is free from the concern about crosstalk, which is highin definition and which does not depend upon the wavelength is possible(see “The foundation of liquid crystal and display application” writtenby Y. Yoshino and M. Ozaki published by CORONA PUBLISHING CO., LTD.)

A method for suppressing the frame response is reducing the potentialdifference between a selection pulse and a non-selection pulse in thesimple matrix drive. As a method for shortening the selection pulseinterval without making the pulse width small, there is a multi-lineselection (MLS). According to the MLS, a plurality of scanning lines isselected simultaneously unlike the conventional line sequential scanning(see Y. Kaneko, et al. “Full Color STN Video LCDs,” Eurodisplay '90Digest, p. 100, 1990).

In the stereoscopic image display apparatus, image information of theplane display device disposed on the back of the optical plate isassigned to respective parallax images. Therefore, the resolution fallsas compared with the original plane display device disposed on the back.Therefore, a function capable of changing over between high definitiontwo-dimensional image display and three-dimensional image displayproviding a stereoscopic sense in the same stereoscopic displayapparatus is desired. In addition, there is also a strong demand for afunction of providing the high definition two-dimensional image displayand the three-dimensional image display on the same display plane, i.e.,a function capable of changing over between a two-dimensional image anda three-dimensional image partially. For implementing changeover betweenthe two-dimensional image and the three-dimensional image partially, itcan provide variable polarization cells, divide electrodes for applyinga voltage to liquid crystal of the variable polarization cells by Xcoordinates and Y coordinates, and apply individual voltages torespective areas.

Drive methods for variable polarization cells can be broadly classifiedinto the following three kinds.

(1) Segment drive

(2) Simple matrix drive

(3) Active matrix drive

The segment drive in (1) is a drive method frequently used in watchesand electronic calculators. Individual display parts (optical switches)are formed of independent electrodes. If matrix drive is conducted,display disturbance is caused in the display part by wiring. Therefore,the segment drive in (1) is not suitable for the drive method ofconducting the changeover between the two-dimensional image and thethree-dimensional image partially.

In the simple matrix drive in (2), matrix drive can be conducted asdescribed above. However, signals input to the same row and the samecolumn are applied in the same way. Therefore, it is necessary to applya voltage of at least a threshold to a pixel only when the pixel isselected and suppress the voltage to the threshold or below when thepixel is not selected. As the resolution (i.e., the number of addresslines in the vertical direction) of the variable polarization cellsbecomes large, the ratio between a voltage applied to liquid crystalwhen the pixel is selected and that when the pixel is not selectedapproaches unity and consequently the selection ratio between thetwo-dimensional image display mode and the three-dimensional imagedisplay mode becomes small. A concrete degradation phenomenon is thatnoise is mixed in the far-side or near-side display at the time of athree-dimensional image display mode because a two-dimensional imagedisplay mode is mixed and the directivity of light rays is degraded. IfTwisted Nematic (TN) liquid crystal obtained by twisting nematic liquidcrystal by 90 degrees is used in the simple matrix drive, then thethreshold characteristics cannot be made sufficiently steep, resultingin a problem that the number of addresses is limited.

If Super Twisted Nematic (STN) having a twist angle of approximately 270degrees and steep threshold characteristics is used instead of TN liquidcrystal, therefore, the contrast can be maintained even when the voltageratio approaches unity. Since the STN liquid crystal has greatdependence of polarization characteristics upon the wavelength, however,it is necessary to use a film which compensates the wavelengthdependence at the time of use and complicated optical design and aretardation film material become necessary.

In the active matrix drive in (3), each pixel is driven individually inone frame section as described above. Therefore, it is possible to useTN liquid crystal. As demerits, however, it can be mentioned that theaperture ratio caused by the black matrix falls (i.e. the luminancefalls) and moire is caused by interference between a black matrix ofvariable polarization cells and a black matrix of an LCD for displaypixel. Furthermore, complication of the manufacture process and a costincrease caused by the manufacture process of the Thin Film Transistor(TFT) can be mentioned.

SUMMARY OF THE INVENTION

The present invention has been made in view of these circumstances, andan object of thereof is to provide a drive method for a stereoscopicimage display apparatus having a function capable of preventingluminance falling and moire occurrence and changing over between atwo-dimensional image and a three-dimensional image partially.

According to an aspect of the present invention, there is provided adrive method for a stereoscopic image display apparatus, thestereoscopic image display apparatus including: a plane display devicehaving a plurality of pixels arranged on a display face; a variablepolarization cell provided in front of the plane display device, thevariable polarization cell including a first electrode substrate havingn (where n≧1) transparent first electrodes arranged in parallel thereon,a second electrode substrate having m (where m≧1) transparent secondelectrodes arranged in a direction substantially perpendicular to thedirection in which the first electrodes are arranged, and liquid crystalsandwiched between the first electrode substrate and the secondelectrode substrate, wherein a polarization direction of light rays fromthe plane display device is made variable according to a voltage appliedbetween the first and second electrode substrates; and an optical plateprovided on an opposite side of the variable polarization cell from theplane display device, the optical plate including a transparentsubstrate, a lens substrate having a plurality of cylindrical lensesarranged thereon so as to have major axes in the same direction, and adouble refraction substance inserted between the transparent substrateand the lens substrate, wherein a major axis direction of the doublerefraction substance is substantially parallel to major axis directionsof lenses of the lens substrate, a minor axis direction of the doublerefraction substance is substantially perpendicular to the major axisdirections of the lenses of the lens substrate, and light rays from thepixels obtained via the variable polarization cell are assigned topredetermined angles, the stereoscopic image display apparatus beingcapable of changing over between a three-dimensional image and atwo-dimensional image and displaying the image, when displaying thethree-dimensional image and the two-dimensional image in a backgroundand a window on a same display plane, the background with one of thethree-dimensional image and the two-dimensional image and displaying afirst to pth (where p≧1) windows with the other image, the drive methodcomprising: setting an ith flag bit (where 1≦i≦p) concerning the firstelectrodes and indicating whether an ith window overlaps the firstelectrodes, and setting an ith flag bit concerning the second electrodesand indicating whether the ith window overlaps the second electrodes;dividing one frame period of the plane display device into p sections asfirst and second pulses of voltage to be applied respectively to thefirst and second electrodes, preparing waveforms of 2^(p) kinds whichdiffer in at least one value of the first and second pulses in thesection obtained by the division, and associating the waveforms with aset of values of the first to pth flag bits concerning the first andsecond electrodes; selecting one first electrode and one secondelectrode respectively from the n first electrodes and the m secondelectrodes; and applying the first and second pulses associated with theset of values of the first to pth flag bits concerning the selectedfirst and second electrodes to the selected first and second electrodes.

According to an aspect of the present invention, there is provided adrive method for a stereoscopic image display apparatus, thestereoscopic image display apparatus including: a plane display devicehaving a plurality of pixels arranged on a display face; a variablepolarization cell provided in front of the plane display device, thevariable polarization cell including a first electrode substrate havingn (where p≧1) transparent first electrodes arranged in parallel thereon,a second electrode substrate having m (where m≧1) transparent secondelectrodes arranged in a direction substantially perpendicular to thedirection in which the first electrodes are arranged, and TN liquidcrystal sandwiched between the first electrode substrate and the secondelectrode substrate, wherein a polarization direction of light rays fromthe plane display device is made variable according to a voltage appliedbetween the first and second electrode substrates; and an optical plateprovided on an opposite side of the variable polarization cell from theplane display device, the optical plate including a transparentsubstrate, a lens substrate having a plurality of cylindrical lensesarranged thereon so as to have major axes in the same direction, and adouble refraction substance inserted between the transparent substrateand the lens substrate, wherein a major axis direction of the doublerefraction substance is substantially parallel to major axis directionsof lenses of the lens substrate, a minor axis direction of the doublerefraction substance is substantially perpendicular to the major axisdirections of the lenses of the lens substrate, and light rays from thepixels obtained via the variable polarization cell are assigned topredetermined angles, the stereoscopic image display apparatus beingcapable of changing over between a three-dimensional image and atwo-dimensional image and displaying the image, when displaying thethree-dimensional image and the two-dimensional image in a backgroundand a window on a same display plane, the background with one of thethree-dimensional image and the two-dimensional image and displaying afirst to pth (where p≧1) windows with the other image, the drive methodcomprising: dividing one frame period of the plane display device into(p+1) sections, applying a pulse of a voltage Va (where Va>0) to allfirst electrodes which overlap the kth window as a first pulse to beapplied to the first electrodes in the kth section (where 1≦k≦p) in thefirst to (p+1)th sections obtained by the division, applying a pulse ofa voltage −Vd (where Vd>0) to all second electrodes which overlap thekth window as a second pulse to be applied to the second electrodes inthe kth section, applying a pulse of a maximum voltage Va to the firstelectrodes which do not overlap any window as a first pulse in the(p+1)th section, and applying a pulse of a voltage Vd to the secondelectrodes which do not overlap any window as a second pulse in the(p+1)th section.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an oblique view showing a stereoscopic image display apparatusto which drive methods according to embodiments are applied;

FIG. 2 is a diagram showing a V-T curve of TN liquid crystal used in avariable polarization cell;

FIG. 3 is a diagram for explaining a state of liquid crystal of avariable polarization cell in a two-dimensional image display mode;

FIG. 4 is a diagram for explaining a state of liquid crystal of avariable polarization cell in a three-dimensional image display mode;

FIG. 5 is a diagram showing dependence of luminance upon an angleobtained when only one elemental image is lit;

FIG. 6 is a diagram showing dependence of a ratio between a centerluminance and a peripheral luminance upon a voltage applied to liquidcrystal;

FIG. 7 is a diagram showing an electrode structure in the simple matrixdrive scheme;

FIG. 8 is a diagram showing an outline of a drive apparatus whichimplements a drive method according to a first embodiment;

FIG. 9 is a diagram for explaining disposition of a window and flag bitsin the first embodiment;

FIG. 10 is a diagram for explaining coordinate conversion between athree-dimensional image viewer and a variable polarization cell in thefirst embodiment;

FIG. 11 is a diagram showing relations among address bit information,column bit information and three-dimensional image display in the firstembodiment;

FIGS. 12( a) and (b) are drive waveform diagrams in the firstembodiment;

FIG. 13 is a diagram showing relations among address bit information,column bit information and three-dimensional image display in the firstembodiment;

FIG. 14 is a drive waveform diagram in the case where there is onewindow which displays a two-dimensional image in a background ofthree-dimensional image display;

FIG. 15 is a diagram for explaining disposition of windows and flag bitsin the first embodiment;

FIG. 16 is a diagram showing relations between drive waveforms appliedto lines and columns and a display mode in the first embodiment;

FIG. 17 is a drive waveform diagram in the first embodiment;

FIG. 18 is a diagram showing relations between drive waveforms appliedto lines and columns and a display mode in the first embodiment;

FIG. 19 is a diagram for explaining disposition of windows and flag bitsin the first embodiment;

FIG. 20 is a drive waveform diagram in the case where there are twowindows which display a three-dimensional image in a background oftwo-dimensional image display;

FIG. 21 is a drive waveform diagram in the case where there are pwindows which display a three-dimensional image in a background oftwo-dimensional image display;

FIG. 22 is a drive waveform diagram in the case where there are pwindows which display a two-dimensional image in a background ofthree-dimensional image display;

FIG. 23 is a drive waveform diagram in the case where there is onewindow which displays a three-dimensional image in a background oftwo-dimensional image display;

FIG. 24 is a drive waveform diagram in the case where there is onewindow which displays a two-dimensional image in a background ofthree-dimensional image display;

FIG. 25 is a diagram showing maximum voltage values of drive waveformsapplied to lines and columns in the second embodiment;

FIG. 26 is a diagram for explaining the case where a plurality ofwindows are disposed in a lattice form; and

FIG. 27 is a diagram showing a shape of an electrode for forming anarbitrary window shape.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Hereafter, embodiments of the present invention will be described withreference to the drawings.

First Embodiment

A drive method for a stereoscopic image display apparatus according to afirst embodiment of the present invention will now be described. Aschematic configuration of the stereoscopic image display apparatusdriven by using the drive method according to the present method isshown in FIG. 1. The stereoscopic image display apparatus according tothe present embodiment includes a plane display device 2 which is, forexample, a liquid crystal display device, a variable polarization cell 4provided in front of the plane display device 2, and an optical plate 6provided on the opposite side of the variable polarization cell 4 fromthe plane display device 2.

The plane display device includes a display face formed by arrangingpixels 2 a each having R (red), G (green) and B (blue) subpixels 2 a ₁,2 a ₂ and 2 a ₃ in a matrix form. The variable polarization cell 4 isprovided in front of the display face. The variable polarization cell 4includes transparent electrode substrates 4 a and 4 b which are opposedto each other. For example, TN (Twisted Nematic) liquid crystal issandwiched between the electrode substrates 4 a and 4 b. Lightilluminated from a pixel of the plane display device 2 is changed inpolarization direction by changing a voltage applied between theelectrode substrates 4 a and 4 b.

The optical plate 6 includes a flat transparent substrate 6 a providedon the variable polarization cell 4 side, a lens substrate 6 b whichcovers the transparent substrate 6 a, and a double refraction substance6 c stored in a region surrounded by the substrate 6 a and the lenssubstrate 6 b. A plurality of cylindrical lenses each having a majoraxis which is nearly perpendicular to a longitudinal arrangementdirection of the pixels 2 a of the plane display device 2 are formed inparallel on the lens substrate 6 b. In other words, the substrate 6 aand the lens substrate 6 b constitute lens frames, and the doublerefraction substance 6 c is stored in the lens frames 6 a and 6 b.Furthermore, a major axis direction of the double refraction substance 6c is nearly parallel to the major axis direction of the lenses of thelens substrate 6 b, and a minor axis direction of the double refractionsubstance 6 c is nearly perpendicular to a major axis direction of eachlens of the lens substrate 6 b. A refractive index of the doublerefraction substance 6 c in the major axis direction is higher than thatin the minor axis direction. Furthermore, the lens frames 6 a and 6 bhave an isotropic refractive index, and it is set so as to be nearlyequal to the refractive index of the double refraction substance 6 c inthe minor axis direction. And the optical plate 6 assigns light raysfrom pixels of the plane display device 2 to predetermined angles.

In the drive method according to the present embodiment, changeoverbetween a two-dimensional image and a three-dimensional image isconducted partially by using the stereoscopic image display apparatushaving such a configuration when displaying the three-dimensional imageand the two-dimensional image on the same display plane. Hereafter, themethod of conducting changeover between a two-dimensional image and athree-dimensional image partially will be described.

The variable polarization cell 4 is brought into a three-dimensionalimage display mode without rotating the light polarization direction byusing TN liquid crystal as the liquid crystal 4 c and applying asaturation voltage Von between the electrode substrates 4 a and 4 b. Byapplying a voltage Voff, the polarization direction of light is rotatedby 90 degrees and the variable polarization cell 4 is brought into atwo-dimensional image display mode.

In the two-dimensional image display mode, the variable polarizationcell 4 conducts adjustment so as to make the polarization direction (adirection of an arrow 11) coincide with minor axis direction of thedouble refraction substance 6 c sandwiched between the substrate 6 a andthe lens substrate 6 b. And the refractive index of the lens frames 6 aand 6 b is isotropic, and set so as to become nearly equal to therefractive index of the double refraction substance 6 c in the minoraxis direction. As a result, light is not bent at an interface betweenthe variable polarization cell 4 and the optical plate 6, and the highdefinition two-dimensional image on the plane display device 2 locatedon the back can be viewed as it is.

On the other hand, in the three-dimensional image display mode, thevariable polarization cell 4 conducts adjustment so as to cause apolarization direction (a direction of an arrow 12) to coincide with themajor axis direction of the double refraction substance 6 c. And therefractive index of the double refraction substance 6 c in the majoraxis direction is higher than the refractive index of the lens frames 6a and 6 b. As a result, light is refracted at the interface between thevariable polarization cell 4 and the optical plate 6 and a lens effectappears. Since light from each pixel of the plane display device 2 isexpanded and illuminated to the whole of the lens face in a directionaccording to each position, a three-dimensional image having directivitycan be viewed.

Restriction conditions concerning the polarization selection ratio willnow be described. As actually measured values which are nearlyproportional to the polarization selection ratio, a V (voltage)-T(transmittance) curve representing voltage dependence at a luminanceobtained when TN liquid crystal sandwiched by the transparent substrateis placed between sheet polarizers which differ from each other inpolarization direction by 90 degrees is known. A rise state of liquidcrystal of the variable polarization cell 4 can be known from the V-Tcurve in the case of normally white. In other words, when no voltage isapplied, molecules do not move at all at the substrate interface. Evenif a voltage which is a certain threshold voltage or below is appliedunder a condition that strong anchoring exists, orientation does notchange at all. If a voltage greater than the threshold voltage isapplied, then the director of the liquid crystal begins to risegradually. If almost all liquid crystal rises, the orientation becomesunchanged.

FIG. 2 shows a typical V-T curve. Hereafter, a measurement method of theV-T curve will be described. In a polarization microscope, sheetpolarizers having a polarization direction which differs from thepolarization direction of the variable polarization cell 4 by 90 degreesare placed above and below a variable polarization cell to beinvestigated. A light source is placed on one of the sheet polarizers,and an analyzer for measuring the luminance is placed on the other ofthe sheet polarizers. The luminance of the analyzer is converted to arelative value, because its absolute value changes according to theenergy of the light source. In a state in which no voltage is applied tothe TN liquid crystal, the polarization direction is twisted by 90degrees because of a twist of the liquid crystal and consequently theluminance of the analyzer side becomes the highest. The luminance inthat state is set to unity, and a relative luminance with respect to themaximum luminance is regarded as the transmittance. If a voltage isapplied to the variable polarization cell, then the liquid crystal risesand consequently the transmittance approaches 0. FIG. 2 is a graphshowing relation between the voltage applied to the variablepolarization cell and the relative luminance, i.e., transmittance of theanalyzer. A voltage at which the luminance becomes 90% in the V-T curveis regarded as a threshold voltage Vth. The threshold voltage Vth iscalculated by using the following expression.

$\begin{matrix}\left( {{Equation}\mspace{14mu} 1} \right) & \; \\{V_{th} = {\pi\sqrt{\frac{1}{ɛ_{0}ɛ_{a}}\left\{ {k_{11} + {\frac{1}{4}\left( {k_{33} - {2\; k_{22}}} \right)}} \right\}}}} & (1)\end{matrix}$

Here, K₁₁ is an elastic constant of spray of the liquid crystal, K₂₂ isan elastic constant of twist of the liquid crystal, K₃₃ is an elasticcoefficient of bend of the liquid crystal, ∈_(a) is a relativedielectric constant of the liquid crystal, and ∈₀ is a relativedielectric constant of the vacuum.

In the two-dimensional image display mode (hereafter referred to as 2Ddisplay mode as well), it is necessary that the polarization directionon the electrode substrate 4 a disposed under the variable polarizationcell 4 and the polarization direction on the electrode substrate 4 bdisposed over the variable polarization cell 4 differ from each other by90 degrees, i.e., the liquid crystal 4 c is twisted by 90 degrees asshown in FIG. 3. In this case, rubbing directions 51 and 52 are formedrespectively on the electrode substrates 4 a and 4 b so as to differfrom each other by 90 degrees and so as to differ by 90 degrees inorientation direction of the liquid crystal as shown in FIG. 3. FIG. 3is a diagram for explaining a state of liquid crystal of a variablepolarization cell in a two-dimensional image display mode. A powersupply 54 applies a voltage less than the threshold voltage Vth betweenthe electrode substrates 4 a and 4 b. The three-dimensional imagedisplay mode (hereafter referred to as 3D display mode as well) needs astate in which the liquid crystal 4 c has almost risen as shown in FIG.4. In this case, the power supply 54 applies a voltage which is at leasta saturation voltage Vsat described later between the electrodesubstrates 4 a and 4 b as shown in FIG. 4. FIG. 4 is a diagram forexplaining a state of liquid crystal of a variable polarization cell ina three-dimensional image display mode.

Association relations between the changeover ratios between thetwo-dimensional image display and the three-dimensional image displayand the V-T curve will now be described with reference to FIGS. 5, 6. Inthe three-dimensional image display mode of an autostereoscopic imagedisplay apparatus, it becomes necessary that one elemental image (animage associated with one cylindrical lens) is illuminated to anarbitrary angle with directivity (FIG. 5). On the other hand, in thetwo-dimensional image display mode, it becomes necessary thatinformation of one pixel is illuminated to all directions withoutdirectivity (FIG. 5).

If TN liquid crystal is used, then a transition region voltage width Δbetween the threshold voltage Vth and the saturation voltage Vsatbecomes wider than that of STN liquid crystal. Therefore, an OFF voltageVoff is at a distance in value from an ON voltage Von. Finding thethreshold voltage Vth of the TN liquid crystal 4 c shown in FIG. 2 onthe basis of Expression (1), both the calculated value and the actuallymeasured value become 1.8 V.

1) In the case of the 2D display mode (the case where V_(2D)<Vth),therefore, the threshold voltage Vth becomes 3.8 V on the basis of thecalculation and FIG. 2. Here, V_(2D) is a voltage applied to thevariable polarization cell 4 when conducting the two-dimensional imagedisplay.

2) In the case of the 3D display mode (the case where V_(3D)<V_(sat)),the saturation voltage V_(sat) becomes 1.8 V on the basis of FIG. 2.Here, V_(3D) is a voltage applied to the variable polarization cell 4when conducting the three-dimensional image display.

Typical simple matrix drive in the variable polarization cell will nowbe described with reference to FIG. 7. Supposing the number of lines inthe vertical direction (scanning lines) Y1 to Yn to be n, one framesection is divided by the number n of lines and a pulse of an addresswaveform for signal waveform selection is generated sequentially for thelines. During a pulse section n of a selected address line, a pulsevoltage having a polarity opposite to that of the pulse voltage on theaddress line is given to a signal line associated with a pixel to beselected to apply a great voltage to the liquid crystal and turn on thedisplay. A pulse voltage having the same polarity as that of the pulsevoltage on the address line is given to a signal line associated with apixel not to be selected to apply a low voltage to the liquid crystaland turn off the display.

Furthermore, since the electro-optic effect of the TN type liquidcrystal is the accumulated response type, its transmittance depends onthe effective value of the applied voltage. In the simple matrix drive,therefore, a column voltage applied to a column (signal line) X1 to Xmis not made equal to 0 V, but it is made equal to the threshold voltageor below when averaged over one frame, even at the time of OFF,resulting in non-display of the liquid crystal. And an important pointof the simple matrix drive technique is that under the condition thatthe average voltage at the time of OFF is made equal to the thresholdvoltage or below, a voltage of at least Vsat at which at least 95% ofthe rise direction of the liquid crystal exists is applied to the liquidcrystal as the ON voltage of the polarization selection ratio.

The simple matrix drive using TN liquid crystal in the drive methodaccording to the present embodiment will now be described with referenceto FIG. 8. FIG. 8 is a diagram showing a concrete example of a drivecircuit which implements the simple matrix drive method. Window rangeinformation is acquired from a PC 21 or a window display part forthree-dimensional image display (not illustrated). Power is suppliedfrom the PC 21 or an external power supply, and a variable regulator 22conducts waveform generation and generation of voltages required forField Programmable Gate Array (FPGA) 23. The FPGA 23 shown in FIG. 8mainly plays roles of two kinds. One of the roles will now be described.For example, when displaying only one window, MUXs (analog switches) arecaused to generate waveforms of two kinds for address signal andwaveforms of two kinds for column signal, i.e., generate voltagewaveforms of four kinds, LINE_ON, LINE_OFF, COLUMN_ON and COLUMN_OFFaccording to the frame frequency on the basis of a voltage generatedfrom a variable regulator 22. In other words, the FPGA 23 causes a MUX24 to generate waveforms of LINE_ON and LINE_OFF at timing according tothe frame frequency, causes a MUX 25 to select one voltage waveform fromthe LINE_ON and LINE_OFF with respect to each line of the variablepolarization cell 4, and applies the selected voltage waveform to anassociated line. The FPGA 23 causes a MUX 26 to generate waveforms ofCOLUMN_ON and COLUMN_OFF at timing according to the frame frequency,causes a MUX 27 to select one voltage waveform from the COLUMN_ON andCOLUMN_OFF with respect to each column of the variable polarization cell4, and applies the selected voltage waveform to an associated column. Asfor the other role, the FPGA 23 classifies ON/OFF lines and columns onthe basis of mode range specification from the PC 21, and conductssignal output waveform selection in each line/column by using as manyMUX 24, 25, 26 and 27 as the total number of lines and columns.

For example, in the case of display of two windows, the FPGA 23 causesthe MUX 24, 25, 26 and 27 to generate waveforms of four kinds foraddress signal and waveforms of four kinds for column signal on thebasis of voltages generated from the variable regulator 22. The casewhere the window display is OFF is represented as 0 and the case wherethe window display is ON is represented as 1. ON/OFF states of displayof the first window (window 1) and display of the second window (window2) are represented as (window 1, window 2). The waveform generationunits 24, 25, 26 and 27 generate voltage waveforms of eight kinds,LINE_(00), LINE_(01), LINE_(10), LINE_(11), COLUMN_(00), COLUMN_(01),COLUMN_(10) and COLUMN_(11) according to the frame frequency. As for theother role, the FPGA 23 classifies lines and columns which assume thestates (00), (01), (10) and (11) on the basis of mode rangespecification from the PC 21, and conducts signal output waveformselection in each line/column by using as many MUXs as the total numberof lines and columns.

Hereafter, features of the drive method in the present embodiment in thecase where three-dimensional image display of a rectangular window isconducted in an arbitrary position and with an arbitrary size when ahigh definition two-dimensional image is displayed on the whole face orthe case where high definition two-dimensional image display of arectangular window is conducted in an arbitrary position and with anarbitrary size when a three-dimensional image is displayed on the wholeface will be described. For simplifying the description, the case whereat least one window concerning a three-dimensional image is displayed inhigh definition two-dimensional image displayed over the whole face willnow be described. The opposite case is conducted in the same way.

(1) It is now supposed that the number of windows is p (≧1). First, as atime period for applying a pulse voltage to an address line, one framesection is divided into p places. The same address waveform signal isinput at coordinates in the vertical axis direction of the same window.

(2) Paying attention to p windows, flag bits for making a decisionwhether the coordinates include each window (whether the coordinatesoverlap each window) as regards the vertical direction and horizontaldirection are transmitted.

(3) Average voltage drive in simple matrix drive is conducted. Theaddress voltage and the column signal voltage assume the same values asthose implementing a maximum contrast. However, the following two pointsare points different from the simple matrix drive method.

(a) In a region where window display of a three-dimensional image is notconducted, the pulse on the address line is not made to rise.

(b) On an address line having a coordinate at which a plurality ofwindows overlap, address pulses also overlap.

The following is supplementary description regarding the above-describedthree items.

(1) The line sequential drive is not used. A flag bit is made to rise tomake a decision whether a certain line includes a window and make adecision whether each window is two-dimensional image display orthree-dimensional image display. A voltage at each timing is selected bya changeover unit.

(2) (m+n)×p data are transmitted. Since selection bits (0 or 1) in m×npolarization directions are not transmitted unlike the simple matrixdrive, there is a merit that the data transfer quantity is small.

In other words, when displaying a background with one of athree-dimensional image and a two-dimensional image and displaying afirst to pth (where p≧1) windows with the other image, the drive methodaccording to the present embodiment includes setting an ith flag bit(where 1≦i≦p) concerning the address lines and indicating whether an ithwindow overlaps the address lines, and setting an ith flag bitconcerning the column lines and indicating whether the ith windowoverlaps the column lines;

dividing one frame period of the plane display device into p sections asfirst and second pulses to be applied respectively to the address linesand the column lines, preparing waveforms of 2^(p) kinds which differ inat least one value of the first and second pulses in the sectionobtained by the division, and associating the waveforms with a set ofvalues of the first to pth flag bits concerning the address lines andthe column lines;

selecting one address line and one column line respectively from the naddress lines and the m column lines; and

applying the first and second pulses associated with the set of valuesof the first to pth flag bits concerning the selected address line andcolumn line to the selected address line and column line.

Thereby, stereoscopic display is conducted partially in p windows, andplane display is conducted in other areas with a resolution equivalentto the display pixels. Or plane display is conducted partially in pwindows with a resolution equivalent to the display pixels, andstereoscopic display is conducted in other areas.

The drive method according to the present embodiment will be describedmore specifically.

First, the case where there is one window of three-dimensional imagedisplay on a background of a high definition two-dimensional image willnow be described. If TN liquid crystal is used in the conventionalsimple matrix drive method, then a transition region voltage width Δ iswide. Therefore, the drive voltage ratio (=Von/Voff) of the variablepolarization cell becomes small as the resolution increases. As aresult, the three-dimensional image display or the two-dimensional imagedisplay is degraded. In order to keep waveform kinds of the address linefew even if the resolution of the variable polarization cell becomeshigh, therefore, places having a window and places having no window aregrouped respectively and the same address waveform is input torespective groups. A merit of this drive method is that the waveformkinds are limited by the number of windows regardless of the increase ofthe resolution of the variable polarization cell. For example, if thenumber of windows is one, each of the address line and the column linehas two kinds. If the number of windows is two, each of the address lineand the column line has four kinds. Hereafter, this will be described.

If there is a window of three-dimensional image display on a part of acertain horizontal line or the whole thereof, “1” is made to rise as aflag bit. If there is no window of three-dimensional image display on acertain horizontal line, “0” is made to rise as a flag bit. In order tomake a distinction between the case where the flag bit is “1” and theflag bit is “0” in waveform, address waveforms of two kinds arerequired.

If there is a window of three-dimensional image display on a part of acertain vertical line or the whole thereof, “1” is made to rise as aflag bit. If there is no window of three-dimensional image display on acertain vertical line, “0” is made to rise as a flag bit.

In the same way, in order to make a distinction between the cases wherethe flag bit is “1” and the flag bit is “0” in waveform, columnwaveforms of two kinds are required.

Supposing that the resolution (the number) of address signal lines is nand the resolution (the number) of column signal lines is m, each linetransmits only information of one bit (0 or 1) and consequently datatransmitted from the PC or a drive device which controlsthree-dimensional image drawing viewer software becomes (m+n) bits intotal as shown in FIG. 9. FIG. 9 is a diagram for explaining dispositionof a window and flag bits in the case where there is one window ofthree-dimensional image display in a background of two-dimensional imagedisplay in the first embodiment. Transmission data bits also requireless information as compared with (m×n) bits required when bitinformation of all resolutions is sent.

As shown in FIG. 9, a window is uniquely determined by left uppercoordinates and right lower coordinates of the window. In many cases,the liquid crystal display device serving as the plane display deviceused when displaying a three-dimensional image has high definition, andthe variable polarization cell need not be higher in definition than thelens pitch. In some cases, therefore, their resolutions do not coincidewith each other. In order to make the window size and position of theliquid crystal display device serving as the plane display device usedwhen displaying a three-dimensional image coincide with those of thevariable polarization cell, therefore, it is necessary to conductcoordinate conversion. This will now be described with reference to FIG.10. FIG. 10 is a diagram for explaining coordinate conversion between athree-dimensional image viewer and a variable polarization cell in thefirst embodiment.

First, the case where origins of the liquid crystal display device andthe variable polarization cell are made to coincide with each other willnow be described. In this case, it is now supposed that left uppercoordinates of a window on the liquid crystal display device whichdisplays a three-dimensional image are (xls, yls), right lowercoordinates of the window are (xle, yle), the width of one pixel is wlp,left upper coordinates of a window on the variable polarization cell are(xhs, yhs), right lower coordinates of the window are (xhe, yhe), andthe width of one pixel is whp. Coordinate conversion can be conductedeasily by using the following expressions. If the width whp of one pixelof the variable polarization cell is set equal to a natural number times(k times) the width wlp of one pixel on the liquid crystal displaydevice which displays a three-dimensional image, then coordinates afterthe conversion become integers and display degradation does not occur,either.xhs=xls/whp×wlp  (2)yhs=yls/whp×wlp  (3)xhe=xle/whp×wlp  (4)yhe=yle/whp×wlp  (5)whp=k×wlpHere, k represents a natural number.

In this way, the polarization direction of the variable polarizationcell is changed so as to be able to display a three-dimensional imagewithout user's burden by linkage with three-dimensional image drawingviewer software.

FIG. 11 is a diagram showing whether to conduct three-dimensional imagedisplay for a pixel when address bit information and column bitinformation are combined with the pixel. If a window of athree-dimensional image is displayed when a two-dimensional image isdisplayed on the whole face, then the display of the three-dimensionalbecomes a logical product of address bit information and column bitinformation.

Drive Waveforms in Case where One Window Displays Three-DimensionalImage

A voltage concerning an address signal is a voltage value applied to oneside of an electrode, and a voltage concerning a column signal becomes avoltage value applied to one side of an electrode. A difference betweenthem becomes voltage amplitude applied to liquid crystal.

Furthermore, one frame period is, for example, 60 Hz drive. Each ofFIGS. 12( a) and 12(b) shows a waveform of half of one frame. FIGS. 12(a) and 12(b) are drive waveform diagrams in the case where there is onewindow which displays a three-dimensional image in a background oftwo-dimensional image display in the first embodiment. In the latterhalf of one frame, the voltage value is inverted. When a voltage isapplied in one direction, therefore, sticking which occurs as thedegradation of liquid crystal can be prevented.

In the address signal shown in FIG. 12( a), a flag of w1 is set to “1”when there is a 3D window on a horizontal line and the flag is set to“0” when there is no 3D window. In the column signal shown in FIG. 12(b) as well, a flag of w1 is set to “1” when there is a 3D window on avertical line and the flag is set to “0” when there is no 3D window.

In the case of “0” in the address waveform, a voltage value is set toVa1“0”=0  (6)

As for the column waveform, the 3D display is OFF in both cases where(address flag, column flag) is (0, 0) and (0, 1) as shown in FIG. 11. Asa result, voltage amplitude of Vth or less is given. Therefore, thecolumn waveform is made to satisfy the following relations.Absolute value(Va1“0”−Vc1“0”)≦VthAbsolute value(Va1“0”−Vc1“1”)≦VthHere, under the condition that the above two expressions are satisfied,maximum limit values of Vc1“0” and Vc1“1” can be found as:Vc1“0”=Vth  (7)Vc1“1”=−Vth  (8)

For making the 3D display OFF when (address flag, column flag) is (1,0), the following relation should be satisfied.Va1“1”−Vc1“0”=Va1“1”−Vd≦VthHere, the following relation can be satisfied.Va1“1”=Vth+Vth=2×Vth  (9)

For making the 3D display ON when (address flag, column flag) is (1, 1),the following relation should be satisfied.Va1“1”−Vc1“1”≧Vsat  (10)Substituting (8) and (9) into (10), we getVa1“1”−Vc1“1”=3×Vth≧Vsat  (11)If Vsat is 3.8 V and Vth is 1.8 V as shown in FIG. 2, then Expression(11) is satisfied and consequently drive at the voltage value ispossible.

In the foregoing description, the upper limit value of Vd is Vd=Vth. Atthat time, it follows that Vsat=5.55 V and it is sufficient forthree-dimensional image display of the polarization selection ratio.

For example, when turning on a shaded area shown in FIG. 9, lines havingY coordinates yhs to yhe to be turned on are provided with 1.8(Vth)×2=3.6 V, other lines are provided with 0 V, columns having Xcoordinates xhs to xhe to be turned on are provided with −1.8 (Vth) V,and other columns (0 to xhs−1, xhe+1 to 15) are provided with +1.8 V.Line selection of this one time corresponds to one frame, and the phaseis reversed in the next frame. The operations are repeated alternately.This is conducted to prevent sticking of the liquid crystal 4 c in thevariable polarization cell 4. In the range to be turned on, the voltagedifference is maximized in the line direction and the column direction.In the range to be turned off, the voltage difference is minimized.

Drive Waveforms in Case where One Window Displays Two-Dimensional Image

The drive waveforms in the case where there is one window which displaysa two-dimensional image on a background of a three-dimensional imagewill now be described. When address bit information and column bitinformation are combined with a certain pixel, the three-dimensionalimage display becomes a logical sum of address bit information andcolumn bit information as shown in FIG. 13. FIG. 13 is a diagram showingrelations among address bit information, column bit information andthree-dimensional image display in the first embodiment.

In the address signal shown in FIG. 14, a flag of w1 is set to “1” whenthere is a 3D window on a horizontal line and the flag is set to “0”when there is no 3D window. In the column signal as well, a flag of w1is set to “1” when there is a 3D window on a vertical line and the flagis set to “0” when there is no 3D window. FIG. 14 is a drive waveformdiagram in the case where there is one window which displays atwo-dimensional image in a background of three-dimensional imagedisplay.

In the case of “0” in the address waveform, a voltage value is set toVa1“0”=−Vth/2  (12)

As for the column waveform, the 3D display is OFF in the case where(address flag, column flag) is (0, 0) as shown in FIG. 13. As a result,voltage amplitude of Vth or less in difference absolute value is given.Therefore, the column waveform is made to satisfy the followingrelation.Absolute value(Va1“0”−Vc1“0”)≦VthHere, as an example, the following relation may be set.Vc1“0”=Vth/2  (13)

Since the 3D display is ON in the case where (address flag, column flag)is (0, 1) as shown in FIG. 13,Absolute value(Va1“0”−Vc1“1”)≦Vsat  (14)Substituting (12) into (14), the lowest limit value of Vc1“1” is foundas follows:−Vth/2−Vc1“1”=VsatTherefore, as an example,Vc1“1”=Vsat−Vth/2  (15)is conceivable. Since the 3D display is OFF in the case where (addressflag, column flag) is (1, 0),Absolute value(Va1“1”−Vc1“0”)≧Vsat  (16)Substituting (15) into (16), and finding the lowest limit value of anabsolute value of Va1“1” for satisfying the relationAbsolute value(Va1“1”−Vth/2)≧Vsat,the relation−(Va1“1”−Vth/2)=−Vsatshould be satisfied.Va1“1”=−Vsat+Vth/2  (17)is conceivable as an example. Finally, since the 3D display is ON in thecase where (address flag, column flag) is (1, 1),Absolute value(Va1“1”−Vc1“1”)≧Vsat  (18)is satisfied. Substituting (15) and (17) into (18), we getVsat−Vth/2−(−Vsat+Vth/2)=2×Vsat−Vth≧VsatSupposing that Vsat is 3.8 V and Vth is 1.8 V, Expression 18 issatisfied, and consequently drive with the above-described voltage valueis possible.

In this case as well, in order to prevent the sticking of the liquidcrystal 4 c of the variable polarization cell 4, the address signalpulse voltage Va repetitively assumes −Vth/2 and Vth/2 alternately andthe column signal pulse voltage Vd repetitively assumes Vth/2 and −Vth/2alternately, when displaying a two-dimensional image in a window. Inareas other than the window for displaying a three-dimensional image,the address signal pulse voltage Va repetitively assumes −(Vsat−Vth/2)and (Vsat−Vth/2) alternately and the column signal pulse voltage Vdrepetitively assumes (Vsat−Vth/2) and −(Vsat−Vth/2) alternately.

Drive Waveforms in Case where there are Two Three-Dimensional ImageDisplay Windows

Drive waveforms in the case where there are two three-dimensional imagedisplay windows on a background of a high definition two-dimensionalimage as shown in FIG. 15 will now be described. FIG. 15 is a diagramfor explaining disposition of windows and flag bits in the case wherethere are two windows which display a three-dimensional image in abackground of two-dimensional image display in the first embodiment.

If there is a window of three-dimensional image display referred to aswindow 1 on a part or the whole of a certain horizontal line (scanningline), then “1” is set as a flag bit. If there is no window ofthree-dimensional image display on a certain horizontal line, then “0”is set as the flag bit. If there is a window of three-dimensional imagedisplay referred to as window 2, then “1” is set as the flag bit. Ifthere is no window of three-dimensional image display on a certainhorizontal line, then “0” is set as the flag bit. As regards each ofwindow 1 and window 2, the waveform is distinguished according towhether the flag bit is “1” or “0” as shown in FIG. 16. FIG. 16 is adiagram showing relations between drive waveforms applied to lines andcolumns and a display mode in the case where there are two windows whichdisplay a three-dimensional image in a background of two-dimensionalimage display in the first embodiment. There are address waveforms offour kinds. In the same way, in the column waveform as well, as regardseach of the window 1 and the window 2, the waveform is distinguishedaccording to whether the flag bit is “1” or “0” as shown in FIG. 17.FIG. 17 is a drive waveform diagram in the case where there are twowindows which display a three-dimensional image in a background oftwo-dimensional image display in the first embodiment. There are columnwaveforms of four kinds. FIG. 17 shows a concrete example of the addresswaveform and the column waveform.

Letting Vth=1.8 V and Vsat=3.8 V and denoting the flag bit of the window1 by w1 and the flag bit of the window 2 by w2, an address signal pulsevoltage Va shown in FIG. 17 is applied according to whether (w1, w2) is(0, 0), (0, 1), (1, 0) or (1, 1).

FIG. 17 shows a waveform of half of a frame. In a latter half of oneframe, the voltage value is inverted. If a voltage is applied in onedirection, therefore, sticking caused by degradation of the liquidcrystal can be prevented. In FIG. 17, half a frame is bisected, and theformer half is provided with a voltage value according to flaginformation of the window 1 and the latter half is provided with avoltage value according to flag information of the window 2.

If one window displays a three-dimensional image, the voltage value maybe the same as the voltage value of drive waveform. In other words, ifthe window 1 is included in a horizontal line, the former half of a halfframe assumesVa“1”=Vth×2  (19)If the window 2 is included in a horizontal line, the latter half of thehalf frame assumesVa“1”=Vth×2In the same way, if the window 1 is not included in a horizontal line,the former half of the half frame assumesVa“0”=0  (20)If the window 2 is not included in a horizontal line, the latter half ofthe half frame assumesVa“0”=0The same holds true as regards the column line as well.If the window 1 is included in a vertical line, the former half of ahalf frame assumesVd“1”=Vth  (21)If the window 2 is included in a vertical line, the latter half of thehalf frame assumesVd“1”=VthIn the same way, if the window 1 is not included in a vertical line, theformer half of the half frame assumesVa“0”=−Vth  (22)If the window 2 is not included in a vertical line, the latter half ofthe half frame assumesVa“0”=−VthThe right side of FIG. 16 shows ON/OFF of the 3D display mode of thewindow 1 and the window 2 when the above-described voltage value isapplied.

In the present example, a pulse voltage shown in FIG. 17 is applied in acertain frame and a voltage obtained by inverting the pulse voltageshown in FIG. 17 (a voltage inverted in sign) is applied in the nextframe, in order to prevent sticking of the liquid crystal 4 c of thevariable polarization cell 4.

The maximum value of the address signal voltage Va is twice the maximumvalue of the data signal voltage Vd. If the maximum value of the datasignal voltage is kept at the threshold voltage Vth or less, the maximumvalue of the difference (=data signal voltage) between the addresssignal and the data signal also becomes the threshold voltage Vth orless.

Since TN liquid crystal is the accumulated response type, voltagedivided in one frame and applied can be calculated as follows:

$\begin{matrix}{{Von}^{2} = {\frac{1}{T}\left\{ {{\left( {{former}\mspace{14mu}{half}\mspace{14mu}{of}\mspace{14mu} V} \right)^{2}\frac{T}{2}} + {\left( {{latter}\mspace{14mu}{half}\mspace{14mu}{of}\mspace{14mu} V} \right)^{2}\frac{T}{2}}} \right\}}} & (23)\end{matrix}$

If the address signal becomes (0, 0) and the column signal becomes (0,0), then the voltage applied to the liquid crystal is Vth over the halfframe. In the same way as the window 1, therefore, the 3D display modebecomes OFF.

A voltage applied to a pixel in a three-dimensional image display frameof the window 2 with the address signal (0, 1) and the column signal(0, 1) is calculated. Expression (24) is obtained.

$\begin{matrix}{{Von}^{2} = {\frac{1}{T}\left\{ {{\left( {V_{a} + V_{d}} \right)^{2}\frac{T}{2}} + {V_{d}^{2}\frac{T}{2}}} \right\}}} & (24)\end{matrix}$Here, T represents one frame period.

Letting Va=3.6 V and Vd=1.8 V, Von becomes 4.02 V and it exceeds thethreshold voltage Vth.

A voltage applied to a pixel located outside a three-dimensional imagedisplay frame of the window 2 with the address signal (0, 1) and thecolumn signal (1, 0) is calculated. Expression (25) is obtained.

$\begin{matrix}{{Voff}^{2} = {\frac{1}{T}\left\{ {{\left( {V_{a} + V_{d}} \right)^{2}\frac{T}{2}} + {V_{d}^{2}\frac{T}{2}}} \right\}}} & (25)\end{matrix}$Letting Va=3.6 V and Vd=1.8 V, Voff becomes 1.8 V and it becomes thethreshold voltage Vth or less.

FIG. 17 shows voltage applied to the liquid crystal during one frame.Drive voltages which satisfy specifications are obtained. If the addresssignal is (1, 1) and the column signal is (1, 1), the followingexpression is satisfied: 3×Vth>Vsat over the half frame. Therefore, thethree-dimensional image display turns on. Since Va is twice Vd, itfollows that Va−Vd=Vd. No matter whether the voltage in the addresswaveform is 0 or Va, if Vd is the same in polarity as Va, i.e., thecolumn waveform is OFF, then the voltage applied to the liquid crystalbecomes the threshold voltage Vth or less, resulting in non-selection.On a line having both the window 1 and the window 2, therefore, thevoltage becomes Va in both the former half and the latter half of theframe. In the case of non-selection in the column waveform (bit 0 in thetwo-dimensional image display mode), however, the voltage applied to theliquid crystal becomes the threshold voltage Vth or less. If the liquidcrystal has poor threshold characteristics, however, the polarizationselection ratio is degraded at Von=4.02 V. In some cases, therefore, thethree-dimensional image display is degraded. In the kind of TN liquidcrystal as well, it is necessary to select TN liquid crystal having agood V-T curve.

Drive Waveform in Case where there are Two Two-Dimensional Image DisplayWindows

A drive waveform in the case where there are two high definitiontwo-dimensional image display windows on a background of athree-dimensional image display will now be described.

If there is a two-dimensional image display window referred to as window1 on a part or the whole of a certain horizontal line, then “0” is setas a flag bit. If there is no two-dimensional image display window on acertain horizontal line, then “1” is set as the flag bit. If there is atwo-dimensional image display window referred to as window 2, then “0”is set as the flag bit. If there is no three-dimensional image displaywindow on a certain horizontal line, then “1” is set as the flag bit. Asregards each of the window 1 and window 2, the waveform is distinguishedaccording to whether the flag bit is “1” or “0” as shown in FIG. 18.There are address waveforms of four kinds. FIG. 18 is a diagram showingrelations between drive waveforms applied to lines and columns and adisplay mode in the case where there are two windows which display atwo-dimensional image in a background of three-dimensional image displayin the first embodiment.

In the same way, in the column waveform as well, as regards each of thewindow 1 and window 2, the waveform is distinguished according towhether the flag bit is “1” or “0” as shown in FIG. 19. FIG. 19 is adiagram for explaining disposition of windows and flag bits in the casewhere there are two windows which display a two-dimensional image in abackground of three-dimensional image display in the first embodiment.There are column waveforms of four kinds. FIG. 20 shows a concreteexample of the address waveform and the column waveform.

Letting Vth=1.8 V and Vsat=3.8 V, an address signal pulse voltage shownin FIG. 20 is applied according to whether (w1, w2) is (0, 0), (0, 1),(1, 0) or (1, 1).

FIG. 20 is a drive waveform diagram in the case where there are twowindows which display a three-dimensional image in a background oftwo-dimensional image display in the first embodiment. FIG. 20 shows awaveform of half of a frame. In a latter half of one frame, the voltagevalue is inverted. If a voltage is applied in one direction, therefore,sticking caused by degradation of the liquid crystal can be prevented.In FIG. 20, the half frame is bisected, and the former half is providedwith a voltage value according to flag information of the window 1 andthe latter half is provided with a voltage value according to flaginformation of the window 2.

If one window displays a two-dimensional image when the whole screen isin the three-dimensional image display state, then the voltage value isdifferent from that of the drive waveform. In other words, if the window1 is included in a horizontal line, 2D display is conducted when theformer half of the half frame is (w1 address flag, w2 address flag, w1column flag, w2 column flag)=(0, 0, 0, 0), (0, 1, 0, 0), (1, 0, 0, 0),(0, 0, 1, 0), (0, 0, 0, 1), (0, 1, 0, 1), (1, 0, 1, 0). In other words,2D display is conducted in a position where the column and address of w1simultaneously become 0 or in a position where the column and address ofw2 simultaneously become 0.

The voltage value shown in FIG. 14 in the case where there is one 2Dwindow differs from that shown in FIG. 20 in the case where there aretwo 2D windows. Because 3D display is conducted when (w1 address flag,w2 address flag, w1 column flag, w2 column flag)=(0, 1, 0, 1) and (1, 0,1, 0).

In the case of two 2D windows, therefore, the following method can betaken. In FIG. 20, different voltage value is assumed according towhether w2 is 0 or 1 when w1 is 0. In other words, the averaged voltagebecomes the threshold voltage or less which brings about the 2D displayor at least the saturation voltage which brings about 3D displayaccording to a combination of w1 and w2. As an example, FIG. 20 can bementioned.

If as regards the flags Va(W1, W2)=(1, 0) and Vd(W1, W2)=(1, 0), then itis meant that the window 1 becomes the 2D display. As shown in FIG. 20,the voltage applied to the address line becomes in the former half ofthe half frameVa(0 to ¼ frame)(1,0)=Vth×2Va(¼ to ½ frame)(1,0)=0After the ½ frame, an inverted voltage is applied in order to preventthe sticking of the liquid crystal.Va(½ to ¾ frame)(1,0)=−Vth×2Va(¾ to 1 frame)(1,0)=0

As shown in FIG. 20, the voltage applied to the column line becomes inthe former half of the half frameVd(0 to ¼ frame)(1,0)=VthVd(¼ to ½ frame)(1,0)=−VthAfter the ½ frame, an inverted voltage is applied in order to preventthe sticking of the liquid crystal.Vd(½ to ¾ frame)(1,0)=VthVd(¾ to 1 frame)(1,0)=−Vth

From the foregoing description, the same voltage value Vth is applied tothe liquid crystal over 0 to ¼ frame and ¼ to ½ frame. As a result, the2D display can be maintained.

If as regards the flags Va(W1, W2)=(1, 0) and Vd(W1, W2)=(0, 1), then itis meant that the window 1 becomes the 2D display. As shown in FIG. 20,the voltage applied to the address line becomes in the former half ofthe half frameVa(0 to ¼ frame)(1,0)=Vth×2Va(¼ to ½ frame)(1,0)=0After the ½ frame, an inverted voltage is applied in order to preventthe sticking of the liquid crystal.Va(½ to ¾ frame)(1,0)=−Vth×2Va(¾ to 1 frame)(1,0)=0

As shown in FIG. 20, the voltage applied to the column line becomes inthe former half of the half frameVd(0 to ¼ frame)(1,0)=−VthVd(¼ to ½ frame)(1,0)=VthAfter the ½ frame, an inverted voltage is applied in order to preventthe sticking of the liquid crystal.Vd(½ to ¾ frame)(1,0)=−VthVd(¾ to 1 frame)(1,0)=Vth

From the foregoing description, Vth×3 is applied to the liquid crystalover 0 to ¼ frame and Vth is applied to the liquid crystal over 0 to ¼frame. Substituting these values into Expression 23, it follows thatVaverage=√5×VthLetting Vth=1.8 V and Vsat=3.8V, it follows thatVaverage=4.02 V>VsatAs a result, 3D display becomes possible.

The combination of w1 and w2 flags and the voltage applied to the liquidcrystal have been shown in FIG. 20. When the window w1 or w2 is OFF, 3Ddisplay is also OFF and desired display can be conducted.

In the present example, a pulse voltage shown in FIG. 20 is applied in acertain frame and a voltage obtained by inverting the pulse voltageshown in FIG. 20 (a voltage inverted in sign) is applied in the nextframe, in order to prevent sticking of the liquid crystal 4 c of thevariable polarization cell 4.

Second Embodiment

A drive method for stereoscopic image display apparatus according to asecond embodiment of the present invention will now be described. Thedrive method according to the present embodiment is used in thestereoscopic image display apparatus shown in FIG. 1 in the same way asthe drive method according to the first embodiment. However, the drivemethod according to the present embodiment differs in the drive methodof the variable polarization cell 4 from the drive method according tothe first embodiment. The drive method according to the presentembodiment is a drive method which maximizes the contrast.

Drive of the variable polarization cell 4 according to the drive methodin the present embodiment will now be described. In the case of onewindow, the waveform differs utterly according to whether there is awindow of three-dimensional image display in a high definitiontwo-dimensional image or there is a window of two-dimensional imagedisplay in a background of a three-dimensional image. Therefore, it isnecessary to prepare five kinds of voltage value inclusive of 0 V. Evenin an address waveform having no window of three-dimensional imagedisplay, however, simpler voltage drive can be conducted by applying anaddress voltage.

Drive Waveforms in Case where there are p (p≧1) Three-Dimensional ImageDisplay Windows

First, drive waveforms in the case where there are p three-dimensionalimage display windows in a high definition two-dimensional image willnow be described.

If there is a three-dimensional image display window on a part or thewhole of a certain horizontal line, then “1” is set as a flag bit. Ifthere is no three-dimensional image display window on a certainhorizontal line, then “0” is set as the flag bit. For making adistinction in waveform between the flag bit “1” and the flag bit “0”,address waveforms of two kinds suffice.

If there is a three-dimensional image display window on a part or thewhole of a certain vertical line, then “1” is set as a flag bit. Ifthere is no three-dimensional image display window on a certain verticalline, then “0” is set as the flag bit. For making a distinction inwaveform between the flag bit “1” and the flag bit “0”, column waveformsof two kinds suffice in the same way.

It is now supposed that a voltage is applied to TN liquid crystal whichforms the variable polarization cell 4, the director of the liquidcrystal begins to rise at a voltage Vth, and the liquid crystal rises95% at a voltage Vsat. In the drive method according to the presentembodiment, the polarization direction is changed as regards p windowareas whereas the polarization direction is not changed as regards areasother than p window areas. On one substrate of two opposed transparentsubstrates of the variable polarization cell 4, n transparent electrodesare disposed in a first direction (for example, in the horizontaldirection). Address line numbers 1 to n are assigned to the ntransparent electrodes. On the other transparent substrate, mtransparent electrodes are disposed in a direction (for example, in thevertical direction) nearly perpendicular to the first direction. Columnline numbers 1 to m are assigned to the m transparent electrodes. Atthis time, in the drive waveforms (address waveforms) for a line in thehorizontal direction, one frame period is divided equally into (p+1)widths. Waveforms corresponding to (p+1) widths each having a maximumvoltage Va are not applied successively in the ascending line number.The same pulse waveform having the voltage value Va in kth width in oneframe is applied to a plurality of lines which overlap kth (where 1≦k≦p)window. The same pulse waveform having the maximum voltage value Va inthe (p+1)th width is applied to lines which do not overlap any window.

On the other hand, as for the column signal lines in the verticaldirection, one frame is divided into (p+1) equal parts. On a columnsignal line which overlaps kth window, the same pulse signal having avoltage value −Vd in the kth part in one frame is applied. The samepulse signal having a voltage value Vd is applied to a column signalline which overlaps a window different from the kth window. In addition,the voltage Vd is always applied to a column signal which does notoverlap any window. By the way, the reason why one frame is divided into(p+1) parts and the above-described drive waveforms are applied is thatliquid crystal which forms the variable polarization cell 4 is TN liquidcrystal and its drive voltage is set by an average value of voltageapplied during one frame period.

A concrete example of drive waveforms applied to address lines andcolumn signal lines at this time is shown in FIG. 21. Address 1 toaddress p respectively indicate voltage waveforms applied to addresslines which overlap the first window to the pth window. When selected, avoltage Va is applied. Otherwise, a voltage of 0 V is applied. Column 1to column p respectively indicate voltage waveforms applied to columnsignal lines which overlap the first window to the pth window. Whenselected, a voltage −Vd is applied. Otherwise, a voltage of +Vd isapplied. Since the address voltage is always applied, drive at themaximum contrast of average voltage drive should be conducted. It is nowsupposed that the threshold voltage is Vth and there are n waveforms forthe address line. According to the document (“The foundation of liquidcrystal and display application” written by Y. Yoshino and M. Ozakipublished by CORONA PUBLISHING CO., LTD), the contrast is maximized,i.e., the polarization selection ratio is maximized by providing Va andVd with values according to the following expressions.

$\begin{matrix}{V_{a} = {\frac{v_{th}}{\sqrt{2}}\sqrt{\frac{1}{1 - \sqrt{\frac{1}{n}}}}}} & (26) \\{V_{d} = {\sqrt{n}V_{a}}} & (27)\end{matrix}$

Drive Waveforms in Case where there are p Two-Dimensional Image DisplayWindows

A concrete example of waveforms in the case where there is a window oftwo-dimensional image display in a background of a three-dimensionalimage is shown in FIG. 22. As shown in FIG. 22, address voltages are thesame as those shown in FIG. 21 and column voltages have waveformsobtained by inverting the column voltages shown in FIG. 21. ComparingFIG. 9 with FIG. 19, there is a difference as to whether the window isthree-dimensional image display (bit 1) or two-dimensional image display(bit 0). In the case where there are p two-dimensional image displaywindows on a background of three-dimensional image display, therefore,the flag bit w1 becomes “0” in the first to pth address drive waveformsincluded in address line drive waveforms, whereas the flag bit w1becomes “1” in the (p+1)-th address drive waveform.

On the other hand, in the case where there is a window ofthree-dimensional image display on a background of high definitiontwo-dimensional image, the flag bit w1 becomes “1” in the first to pthaddress drive waveforms, whereas the flag bit w1 becomes “0” in the(p+1)-th address drive waveform.

In the present embodiment, drive waveforms in the case where there isone window of three-dimensional image display on a background of a highdefinition two-dimensional image are shown in FIG. 23.

In the present embodiment, drive waveforms in the case where there isone window of two-dimensional image display on a background ofthree-dimensional image display are shown in FIG. 24.

Va and Vd of the liquid crystal having the V-T curve shown in FIG. 2 atthe time when there are n address drive waveforms are calculated byusing Expression 26 and Expression 27. And a voltage applied to theliquid crystal on an average is calculated. A result is shown in FIG.25. Even in the case where the difference between Va and Vd is small soas to satisfy the relation Va−Vd<Vd, the case where there is a window ofthree-dimensional image display on high definition two-dimensional imagedisplay, and the case where Va is applied to a plurality of pulses inaddress lines, partial three-dimensional image display free from displaydegradation can be conducted. If Vd has the same polarity as Va, i.e.,the column drive waveform is OFF regardless of whether the voltage is 0V or Va in the address drive waveform, then the voltage applied to theliquid crystal becomes the threshold voltage or below resulting in anunselected state. On a line which overlap both the window 1 and thewindow 2, the applied voltage becomes Va in both the former half and thelatter half of the frame. In the case of non-selection in the columnwaveform (the two-dimensional image display mode and the flag bit is“0”), the voltage applied to the liquid crystal becomes the thresholdvoltage or below.

If the kth window which changes the polarization direction exists on acertain line and the kth window exists on the same column lines on thecertain line, the lines or the columns are made not to be adjacent areasbut be discrete. As a result, a plurality of windows is formed in agrating form. An example of distribution of windows on the variablepolarization cell 4 in this case is shown in FIG. 26.

When displaying a 3D display window in one place in a 2D display window,flags 1 of windows 1 are typically set consecutively only in a certainrange of the address lines and column lines. As indicated by windows 1in FIG. 26, it is also possible to set flags 1 of windows 1 so as to bedivided into a plurality of places and consecutive only in certainranges. In that case, in places where flags of address lines and columnlines are set to 1 in areas of the window 1, a part in which the logicalproduct of an address line and a column line is 1 becomes 3D display.For example, if flags of each of address lines and column lines are setto 1 in two places, 3D display of 2×2=4 windows becomes possible.

The simple matrix drive is effective in a rectangular window. In awindow having an arbitrary shape such as an ellipse or a rhombus, thenumber and positions of pixels used for three-dimensional image displayare not determined uniquely in a window of each address line. Therefore,the number pf address drive waveforms becomes large, and the ON/OFFvoltage ratio, i.e., the polarization selection ratio becomes small,resulting in degraded three-dimensional image display. If an area wherea three-dimensional image is to be displayed is predetermined,therefore, it becomes possible to display a window of an arbitrary shapeby providing the transparent electrode with a shape of an ellipse or arhombus beforehand as shown in FIG. 27.

According to the embodiments of the present invention, it becomespossible to prevent luminance falling and moire occurrence and changeover between a two-dimensional image and a three-dimensional imagepartially.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcepts as defined by the appended claims and their equivalents.

1. A drive method for a stereoscopic image display apparatus, the stereoscopic image display apparatus including: a plane display device having a plurality of pixels arranged on a display face; a variable polarization cell provided in front of the plane display device, the variable polarization cell including a first electrode substrate having n (where n≧1) transparent first electrodes arranged in parallel thereon, a second electrode substrate having m (where m≧1) transparent second electrodes arranged in a direction substantially perpendicular to the direction in which the first electrodes are arranged, and liquid crystal sandwiched between the first electrode substrate and the second electrode substrate, wherein a polarization direction of light rays from the plane display device is made variable according to a voltage applied between the first and second electrode substrates; and an optical plate provided on an opposite side of the variable polarization cell from the plane display device, the optical plate including a transparent substrate, a lens substrate having a plurality of cylindrical lenses arranged thereon so as to have major axes in the same direction, and a double refraction substance inserted between the transparent substrate and the lens substrate, wherein a major axis direction of the double refraction substance is substantially parallel to major axis directions of lenses of the lens substrate, a minor axis direction of the double refraction substance is substantially perpendicular to the major axis directions of the lenses of the lens substrate, and light rays from the pixels obtained via the variable polarization cell are assigned to predetermined angles, the stereoscopic image display apparatus being capable of changing over between a three-dimensional image and a two-dimensional image and displaying the image, when displaying the three-dimensional image and the two-dimensional image in a background and a window on a same display plane, the background with one of the three-dimensional image and the two-dimensional image and displaying a first to pth (where p≧1) windows with the other image, the drive method comprising: setting an ith flag bit (where 1≦i≦p) concerning the first electrodes and indicating whether an ith window overlaps the first electrodes, and setting an ith flag bit concerning the second electrodes and indicating whether the ith window overlaps the second electrodes; dividing one frame period of the plane display device into p sections as first and second pulses of voltage to be applied respectively to the first and second electrodes, preparing waveforms of 2^(p) kinds which differ in at least one value of the first and second pulses in the section obtained by the division, and associating the waveforms with a set of values of the first to pth flag bits concerning the first and second electrodes; selecting one first electrode and one second electrode respectively from the n first electrodes and the m second electrodes; and applying the first and second pulses associated with the set of values of the first to pth flag bits concerning the selected first and second electrodes to the selected first and second electrodes.
 2. The method according to claim 1, wherein the liquid crystal of the variable polarization cell is TN liquid crystal, and denoting a voltage at which a director of the liquid crystal begins to rise by Vth and a voltage at time when the liquid crystal has risen 95% by Vsat, a relation Vsat<Vth×3 is satisfied, when performing two-dimensional image display on the background and the number of the windows which perform three-dimensional image display is one, voltages of Vth×2 and −Vth×2 are alternately applied to the first electrodes overlapping the window, and voltage of 0 V is applied to the first electrodes which do not overlap the window, and voltages of Vth and −Vth are alternately applied to the second electrodes overlapping the window, and voltages of −Vth and Vth are alternately applied to the second electrodes which do not overlap the window.
 3. The method according to claim 1, wherein the liquid crystal of the variable polarization cell is TN liquid crystal, and denoting a voltage at which a director of the liquid crystal begins to rise by Vth and a voltage at time when the liquid crystal has risen 95% by Vsat, a relation Vsat<Vth×3 is satisfied, when performing three-dimensional image display on the background and the number of the windows which perform two-dimensional image display is one, voltages of −Vth/2 and Vth/2 are alternately applied to the first electrodes overlapping the window, and voltages of −(Vsat−Vth/2) and (Vsat−Vth/2) are alternately applied to the first electrodes which do not overlap the window, and voltages of Vth/2 and −Vth/2 are alternately applied to the second electrodes overlapping the window, and voltages of −(Vsat−Vth/2) and (Vsat−Vth/2) are alternately applied to the second electrodes which do not overlap the window.
 4. The method according to claim 1, wherein the liquid crystal of the variable polarization cell is TN liquid crystal, and a voltage at which a director of the liquid crystal begins to rise is denoted by Vth (V), when two-dimensional image display is performed on the background and the windows which perform three-dimensional image display are first and second windows, a voltage of 2×Vth is applied to the first electrodes which overlap only the first window over a former half of the one frame and a voltage of 0 V is applied to the first electrodes which overlap only the first window over a latter half of the one frame, a voltage of 0 V is applied to the first electrodes which overlap only the second window over a former half of the one frame and a voltage of 2×Vth is applied to the first electrodes which overlap only the second window over a latter half of the one frame, a voltage of 2×Vth is applied to the first electrodes which overlap both the first and second windows over both the former half and the latter half of the one frame, a voltage of 0 V is applied to the first electrodes which overlap neither the first nor the second windows over both the former half and the latter half of the one frame, a voltage of −Vth is applied to the second electrodes which overlap only the first window over a former half of the one frame and a voltage of Vth is applied to the second electrodes which overlap only the first window over a latter half of the one frame, a voltage of Vth is applied to the second electrodes which overlap only the second window over a former half of the one frame and a voltage of −Vth is applied to the second electrodes which overlap only the second window over a latter half of the one frame, a voltage of −Vth is applied to the second electrodes which overlap both the first and second windows over both the former half and the latter half of the one frame, and a voltage of Vth is applied to the second electrodes which overlap neither the first nor the second windows over both the former half and the latter half of the one frame.
 5. The method according to claim 1, wherein the liquid crystal of the variable polarization cell is TN liquid crystal, a voltage at which a director of the liquid crystal begins to rise is denoted by Vth (V), and a voltage at which the liquid crystal has risen to 95% is denoted by Vsat, when three-dimensional image display is performed on the background and the windows which perform two-dimensional image display are first and second windows, a voltage of 0 V is applied to the first electrodes which overlap only the first window over a former half of the one frame and a voltage of 2×Vth is applied to the first electrodes which overlap only the first window over a latter half of the one frame, a voltage of 2×Vth is applied to the first electrodes which overlap only the second window over a former half of the one frame and a voltage of 0 V is applied to the first electrodes which overlap only the second window over a latter half of the one frame, a voltage of 0 V is applied to the first electrodes which overlap both the first and second windows over both the former half and the latter half of the one frame, a voltage of Vsat+Vth is applied to the first electrodes which overlap neither the first nor the second windows over both the former half and the latter half of the one frame, a voltage of −Vth is applied to the second electrodes which overlap only the first window over a former half of the one frame and a voltage of Vth is applied to the second electrodes which overlap only the first window over a latter half of the one frame, a voltage of Vth is applied to the second electrodes which overlap only the second window over a former half of the one frame and a voltage of −Vth is applied to the second electrodes which overlap only the second window over a latter half of the one frame, a voltage of Vth is applied to the second electrodes which overlap both the first and second windows over both the former half and the latter half of the one frame, and a voltage of −(Vsat+Vth) is applied to the second electrodes which overlap neither the first nor the second windows over both the former half and the latter half of the one frame.
 6. The method according to claim 2, wherein when sheet polarizers which differ in polarization direction by 90 degrees are placed on both sides of the variable polarization cell, the voltage Vth is measured as a threshold voltage at which transmittance from one of the sheet polarizers to the other becomes 90%, and when sheet polarizers which differ in polarization direction by 90 degrees are placed on both sides of the variable polarization cell, the voltage Vsat is measured as a voltage at which transmittance from one of the sheet polarizers to the other becomes 2%.
 7. A drive method for a stereoscopic image display apparatus, the stereoscopic image display apparatus including: a plane display device having a plurality of pixels arranged on a display face; a variable polarization cell provided in front of the plane display device, the variable polarization cell including a first electrode substrate having n (where p≧1) transparent first electrodes arranged in parallel thereon, a second electrode substrate having m (where m≧1) transparent second electrodes arranged in a direction substantially perpendicular to the direction in which the first electrodes are arranged, and TN liquid crystal sandwiched between the first electrode substrate and the second electrode substrate, wherein a polarization direction of light rays from the plane display device is made variable according to a voltage applied between the first and second electrode substrates; and an optical plate provided on an opposite side of the variable polarization cell from the plane display device, the optical plate including a transparent substrate, a lens substrate having a plurality of cylindrical lenses arranged thereon so as to have major axes in the same direction, and a double refraction substance inserted between the transparent substrate and the lens substrate, wherein a major axis direction of the double refraction substance is substantially parallel to major axis directions of lenses of the lens substrate, a minor axis direction of the double refraction substance is substantially perpendicular to the major axis directions of the lenses of the lens substrate, and light rays from the pixels obtained via the variable polarization cell are assigned to predetermined angles, the stereoscopic image display apparatus being capable of changing over between a three-dimensional image and a two-dimensional image and displaying the image, when displaying the three-dimensional image and the two-dimensional image in a background and a window on a same display plane, the background with one of the three-dimensional image and the two-dimensional image and displaying a first to pth (where p≧1) windows with the other image, the drive method comprising: dividing one frame period of the plane display device into (p+1) sections, applying a pulse of a voltage Va (where Va>0) to all first electrodes which overlap the kth window as a first pulse to be applied to the first electrodes in the kth section (where 1≦k≦p) in the first to (p+1)th sections obtained by the division, applying a pulse of a voltage −Vd (where Vd>0) to all second electrodes which overlap the kth window as a second pulse to be applied to the second electrodes in the kth section, applying a pulse of a maximum voltage Va to the first electrodes which do not overlap any window as a first pulse in the (p+1)th section, and applying a pulse of a voltage Vd to the second electrodes which do not overlap any window as a second pulse in the (p+1)th section.
 8. The method according to claim 7, wherein the voltage Va and the voltage Vd satisfy the following expressions. $\begin{matrix} {V_{a} = {\frac{v_{th}}{\sqrt{2}}\sqrt{\frac{1}{1 - \sqrt{\frac{1}{n}}}}}} \\ {V_{d} = {\sqrt{n}V_{a}}} \end{matrix}$ 